Control of networks of Euler-Bernoulli beams

Bertrand Dekoninck; Serge Nicaise

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 57-81
  • ISSN: 1292-8119

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Dekoninck, Bertrand, and Nicaise, Serge. "Control of networks of Euler-Bernoulli beams." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 57-81. <http://eudml.org/doc/90556>.

@article{Dekoninck1999,
author = {Dekoninck, Bertrand, Nicaise, Serge},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Petrovsky systems; hyperbolic systems; networks of Euler-Bernoulli beams; multiplier method; Ingham's inequality; exact controllability},
language = {eng},
pages = {57-81},
publisher = {EDP Sciences},
title = {Control of networks of Euler-Bernoulli beams},
url = {http://eudml.org/doc/90556},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Dekoninck, Bertrand
AU - Nicaise, Serge
TI - Control of networks of Euler-Bernoulli beams
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 57
EP - 81
LA - eng
KW - Petrovsky systems; hyperbolic systems; networks of Euler-Bernoulli beams; multiplier method; Ingham's inequality; exact controllability
UR - http://eudml.org/doc/90556
ER -

References

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  1. [1] F. AliMehmeti, A characterisation of generalized C∞ notion on nets. Int. Eq. and Operator Theory 9 ( 1986) 753-766. Zbl0617.35022MR866963
  2. [2] F. AliMehmeti, Regular solutions of transmission and interaction problems for wave equations. Math. Meth. Appl. Sci. 11 ( 1989) 665-685. Zbl0722.35062MR1011812
  3. [3] J.M. Ball and M. Slemrod, Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems. Comm. Pure Appl. Math. 32 ( 1979) 555-587. Zbl0394.93041MR528632
  4. [4] J. von Below, A characteristic equation associated to an eigenvalue problem on c2-networks. Linear Alg. Appl. 71 ( 1985) 309-325. Zbl0617.34010MR813056
  5. [5] J. von Below, Classical solvability of linear parabolic equations on networks. J. Diff. Eq. 72 ( 1988) 316-337. Zbl0674.35039MR932369
  6. [6] J. von Below, Sturm-Liouville eigenvalue problems on networks. Math. Meth. Appl. Sci. 10 ( 1988) 383-395. Zbl0652.34025MR958480
  7. [7] J. von Below, Parabolic Network Equations. Habilitation Thesis, Eberhard-Karls-Universität Tübingen ( 1993). Zbl0833.35072
  8. [8] J. von Below and S. Nicaise, Dynamical interface transition with diffusion in ramified media. Comm. Partial Diff. Eq. 21 ( 1996) 255-279. Zbl0852.35057MR1373774
  9. [9] A. Borovskikh, R. Mustafokulov, K. Lazarev and Yu. Pokornyi, A class of fourth-order differential equations on a spatial net. Doklady Math. 52 ( 1995) 433-435. Zbl0891.34018
  10. [10] G. Chen, M. Delfour, A. Krall and G. Payre, Modelling, stabilization and control of serially connected beams. SIAM J. Control and Opt. 25 ( 1987) 526-546. Zbl0621.93053MR885183
  11. [11] G. Chen, S. Krantz, D. Russell, C. Wayne, H. West and M. Coleman, Analysis, design, and behavior of dissipative joints for coupled beams. SIAM J. Appl. Math. 49 ( 1989) 1665-1693. Zbl0685.73046MR1025953
  12. [12] G. Chen and J. Zhou, The wave propagation method for the analysis of boudary stabilization in vibrating structures, SIAM J. Appl. Math. 50 ( 1990) 1254-1283. Zbl0712.73069MR1061349
  13. [13] P.G. Ciarlet, H. Le Dret and R. Nzengwa, Junctions between three-dimension and two-dimensional linearly elastic structures. J. Math. Pures Appl. 68 ( 1989) 261-295. Zbl0661.73013MR1025905
  14. [14] F. Conrad, Stabilization of vibrating beams by a specific feedback, A.V. Balakrishnan and J.P. Zolésio Eds., Stabilization of flexible structures, Opt. Software Inc. ( 1988) 36-51. Zbl0774.93069
  15. [15] B. Dekoninck and S. Nicaise, The eigenvalue problem for networks of beams. Preprint LIMAV 96-9, University of Valenciennes, Linear Alg. Appl. (submitted). Zbl0979.74026MR1678648
  16. [16] P. Grisvard, Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 21 (Pitman, Boston, 1985). Zbl0695.35060MR775683
  17. [17] P. Grisvard, Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités. J. Math. Pures Appl. 68 ( 1989) 215-259. Zbl0683.49012MR1010769
  18. [18] A.E. Ingham, Some trigonometrical inequalities with applications in the theory of series. Math. Z. 41 ( 1936) 367-369. Zbl0014.21503MR1545625
  19. [19] V. Komornik, Exact controllability and stabilization. The multiplier method. RM A 36 Masson, Paris ( 1994). Zbl0937.93003MR1359765
  20. [20] J.E. Lagnese, Modeling and controllability of plate-beam systems. J. Math. Systems, Estimation and Control. 5 ( 1995) 141-187. Zbl0854.93072MR1321097
  21. [21] J.E. Lagnese, G. Leugering and E.J.P.G. Schmidt, Modeling of dynamic networks of thin thermoelastic beams. Math. Meth. Appl. Sci. 16 ( 1993) 327-358. Zbl0773.73060MR1217432
  22. [22] J.E. Lagnese, G. Leugering and E.J.P.G. Schmidt, Control of planar networks of Timoshenko beams. SIAM J. Cont. Opt. 31 ( 1993) 780-811. Zbl0775.93107MR1214764
  23. [23] J.E. Lagnese, G. Leugering and E.J.P.G. Schmidt, Modeling, analysis and control of dynamic elastic multi-link structures, Birkhäuser, Boston ( 1994). Zbl0810.73004MR1279380
  24. [24] H. Le Dret, Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications. RMA 19, Masson, Paris ( 1991). Zbl0744.73027MR1130395
  25. [25] G. Leugering and E.J.P.G. Schmidt, On the control of networks of vibrating strings and beams, in Proc. of the 28th IEEE Conference on Decision and Control, Vol. 3, IEEE ( 1989) 2287-2290. 
  26. [26] J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1, RMA 8, Masson, Paris ( 1988). Zbl0653.93002MR953547
  27. [27] S. Nicaise, Exact controllability of a pluridimensional coupled problem. Rev. Math. Univ. Complutense Madrid 5 ( 1992) 91-135. Zbl0760.35012MR1183428
  28. [28] S. Nicaise, About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation II: Exact controllability. Ann. Scuola Normale Sup. Pisa, Series IV 20 ( 1993) 163-191. Zbl0815.73035MR1233635
  29. [29] S. Nicaise, Boundary exact controllability of interface problems with singularities I: Addition of the coefficients of singularities. SIAM J. Contr. Opt. 34 ( 1996) 1512-1533. Zbl0858.93012MR1404844
  30. [30] S. Nicaise, Boundary exact controllability of interface problems with singularities II: Addition of internal controls. SIAM J. Contr. Opt. 35 ( 1997) 585-603. Zbl0872.93038MR1436640
  31. [31] J.P. Puel and E. Zuazua, Exact controllability for a model of multidimensional flexible structure. Proc. Royal Soc. Edinburgh 123 A ( 1993) 323-344. Zbl0925.93087MR1215417
  32. [32] E.J.P.G. Schmidt, On the modelling and exact controllability of networks of vibrating strings. SIAM J. Contr. Opt.30 ( 1992) 229-245. Zbl0755.35008MR1145715

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